$4\mathrm{.}41$ List the cosets of each of the following q$-$ary linear codes:

$($a$)$ q $=3$ and C$3=\{0000,1010,2020,0101,0202,1111,1212,2121,2222\},$

$($b$)$ q $=2$ and C$2=\{00000,10001,01010,11011,00100,10101,01110,11111\}.$